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Abstract

Stress analysis plays important role in the structural integrity and optimization. Prior stress estimation helps in better design of the products. Composites find wide usage in the industrial and home applications due to its strength to weight ratio. Especially in the air craft industry, the usage of composites is more due to its advantages over the conventional materials. Composites are mainly made of orthotropic materials having unequal strength in the different directions. Composite materials has the drawback of delamination and debonding due to the weaker bond materials compared to the parent materials. So proper analysis should be done to the composite joints before using it in the practical conditions. In the present work, a composite plate with elastic pin is considered for analysis using finite element software Ansys. Initially the geometry is built using Ansys software using top down approach with different Boolean operations. The modeled object is meshed with 3 dimensional layered element solid46 for composite plate and structural three dimensional solid element Solid45 for pin material. Various combinations are considered to find the strength of the composite joint under uniaxial loading conditions. Due to symmetry of the problem, only quarter geometry is built and results are presented for full model using Ansys expansion options. The results show effect of pin diameter on the joint strength. Here the deflection and load sharing of the pin is increasing and other parameters like overall stress, pin stress and contact pressure is reducing due to lesser load on the plate material. Further material effect shows, higher young modulus material has little deflection, but other parameters are increasing. Interference analysis shows increasing of overall stress, pin stress, contact stress along with pin bearing load. This increase should be understood properly for increasing the load carrying capacity of the joint. Generally every structure is preloaded to increase the compressive stress in the joint to increase the load carrying capacity. But the stress increase should be properly analysed for composite due to its delamination and debonding effects due to failure of the bond materials. When results for an isotropic combination is compared with composite joint, isotropic joint shows uniformity of the results with lesser values for all parameters. This is mainly due to applied layer angle combinations. All the results are represented with necessasary pictorial plots.

KEYWORDS

I. INTRODUCTION

In this section, we examine the problem of composite laminates with an elastically pinned circular hole. The effects of
friction and bearing load on the stress redistribution are studied in detail, based on the infinite plate configuration. The
issues of practical interest, such as the loading-history and cycling dependencies of stress state due to the presence of
friction, are addressed. The material properties and the numerical meshes used in the simulation are described below.
The laminate plate contains seven plies of identical orthotropic material with the stacking sequence (0/±45/90ˉ)s. The
orthotropic material represents a unidirectional fiber-reinforced composite plate. With the fibers lying in the horizontal
plane (Lubin, 1982). The number in the stacking sequence indicates the in-plane rotation angle of each ply relative to
the reference 0o-ply where the fibers lie in the 0o direction. The elastic constants are given by E1=138 GPa, E2 = E3
=14.5 GPa, μ23= μ13= μ12=5.86 GPa, and ν23=ν13=ν12=0.21. Meanwhile, the isotropic pin is made of Ti–6Al–4V, and the elastic constants are given by Ef =110 GPa, and ν=0.31. The hole radius R is taken to be the normalization length scale.
The plate thickness H = 1.4R, i.e., ply thickness = 0.2R. The length of the pin is 2R.

Note that the elements and nodes on the hole surface match with those on the vertical surface of the pin. The nodes on
the hole surface and those on the pin surface are numbered separately.The mesh used in the simulation is described as
follows. The hole surface is discretized with equal divisions in the thickness direction (i.e., six vertical divisions per
ply). The elements are of the constant type, assuming uniform fields in each element and with a single node located at
the center. The vertical surface of the pin is discretized, among these elements, those between the plate surfaces are in
one-to-one correspondence with those on the hole surface. The top and bottom surfaces of the pin are discretized with
same pattern.

II. LITERATURE REVIEW

Chen et al. [1] analyzed 3D contact stress in the mechanical joints of symmetric composite material layers by numerical
method. Their results were accomplished using local contact between pin and hole, considering 3D friction and
clearance.

Tayfun Gulem et.al.[3] carried out a study to deal with the bearing strength, failure mode and failure load in a woven
laminated glass vinyl ester composite plate with circular hole subjected to a traction force by a rigid pin. They
investigated for two variables; the distance from the free edge of the plate to- the diameter of the hole (E/D) ratio and
the width of rectangular plate-to-the diameter of the hole (W/D) ratio numerically and experimentally.

McCarthi et al. [4] investigated clearance effects on stress distribution for multiple pin joint, by use of FEM and
MARC software. Yavari and Kadivar [5] studied the effects of contact surface between pin and shell in mechanical
single edge “composite” materials by use of ABAQUS software. In this research, they considered 3D joint behavior
and also friction effect. Wimmer and Pettermann [6] numerically simulated separation in composite plates. In his study,
he used combination of critical and failure loadings. Alenfaie [7] modeled composite plates with internal separation
plates by use of finite element method. He used a 3D model and calculated natural frequency and displacement in
various cases.

Yang et al. [8] defined exact numerical method for mechanical behavior of composite plates with elastic joints. They
assumed isotropic joints and also considered friction in contact surface between joints and plates. In their analysis,
plates were assumed symmetric. Hyer and Liu (1984) investigated effect of pin elasticity, clearance and friction on
radial and tangential stress distribution around hole in mechanical joints of orthotropic plates by numerical method.
Their model was 2D and constituted of two symmetric layers to investigate aforementioned parameters.

III. EXPERIMENTAL PROCEDURE

Steps carried out for Modeling

Step 1: Mesh the plate with circular hole of radius 5mm, without any triangular element at the circular region.

Step 2: Now create the laminate of desired thickness, by dragging the elements along Z directions with required
number of layers along the ply thickness (Ex: 6 layers/ Ply).

Step 3: Create 7 ply’s of same thickness, by dragging it along Z direction, as shown in Fig 1.

Step 4: Create separate collector with desired name for each ply, and move those elements to newly created collector.

Step 5: Create mesh at the top of the pin face, and project those elements to top of the ply plane, then create elements
by drag option. While creating pin elements nodes on circumference of pin should match with those nodes on the ply
hole face and extend the elements of pin to the desired length on either sides

Step 6: Create a rigid at one end of the composite plate by selecting all the nodes to apply a single point load on it.

Step 7: Create constrain (all degrees fixed) at the other end of the composite plate and at top and bottom of the pin, as
shown in Fig.2.

Step 8: Create material property for Composite plate and Pin.

Step 9: Create property for each ply with desired ply orientations along with the thickness and assign to respective ply.

Step 10: Apply desired load on the centre node of the rigid.

Step 11: Define contact between pin and composite plate interface with the frictional value of 0.3, by selecting nodes
on plate hole face and pin surface at the contact region.

Step 12: Submit the run in Ansys and post process the result.

Above figure shows Elements creation to represent composite plate of 7 ply’s by mesh the plate with circular hole of
radius 5mm, without any triangular element at the circular region. Now create the laminate of desired thickness, by
dragging the elements along Z directions with required number of layers along the ply thickness (Ex: 7layers/ Ply).

Above shown image describe the complete model with 7 layers of laminates and a pin

IV. PROBLEM DEFINITION

Analysis has been carried out for different load cases. The analysis is very important as the pin joints are used in many
structures. Any improvement in the stress reduction helps in fatigue life improvement of the machine components and
joints. So an finite element analysis is carried out to find the joint behaviour under various conditions of the pin for the
composite plate. The following cases of analysis are carried out.

Case 1: Diameter effect on stress generation

Case 2: Pin material effect on the stress generation

Case 3: Comparison for Isotropic and composite joint

V. EXPERIMENTAL RESULTS

VI. CONCLUSION

We have proposed an efficient and accurate analytical method for analyzing the mechanical behavior of a composite
laminate plate with an elastically pinned circular hole under a bearing force on the pin. The composite laminates are
considered to be generally Orthotropic and the pin to be isotropic. The plies are assumed to be perfectly bonded. The
contact interaction between the composite and pin is followed by a Eulirian algorithm. The overall summary of the
analysis is as follows.

Initially Modeling is done using Ansys preprocessor. Initially blocks are built and copied to the required size to ease
brick meshing of the problem. Boolean operations are used to build hole in the solid blocks. Contacts are defined
between plate and the pin after selecting target and contact regions using Targe170 and Contac174 elements. Standard contact algorithms are selected for better accuracy. After application of boundary conditions, the analysis is carried
out for various load cases.

Initially analysis is carried out to find the effect of pin diameter on joint behaviour. The pin diameters are changed from
5mm to 7mm with increment of 1mm. The results are captured for Deformation, overall stress, pin stress, contact
pressure and pin bearing load. The results shows increase of deformation and bearing load with increase in the
diameter along with reduction of stress in both plate and pin materials. Also contact pressure is dropping with the
increase in the diameter. This can be mainly attributed to increased contact area which reduces the stresses in the
overall joint.

Further analysis is carried out with variation of materials (Young’s Modulus ‘E’) and results are captured for
deformation, Vonmises stress, contact pressure, pin stress and bearing loads. The results shows higher effect of
young’s modulus on the behaviour of the joint. Increase in the young’s modulus is increasing all the design parameters
excepting the deformation. This can be mainly attributed to increased stiffness with the higher young’s modulus
materials. Higher stresses are not desirable in the composite plates, as they are potential sources of stress concentration
and possible sources for delamination debonding effects.

Final analysis with isotropic combination shows better load distribution with compared to the composite material. For
the same external load, all the values (Deformation, overall Vonmises stress, pin stress, contact pressure and pin
bearing load) are less compared to the composite plate. The aim of the project is not to show the advantages or strength
of composite over the isotropic combinations, but to analyze the composite plate with elastic pin interface conditions
for overall stress and load distribution conditions.